1Thanxxx......sir........
Let f(x) =2007^{x}/(2007^{x}+\sqrt{2007}) then the sum f(1/2007) +f(2/2007)+.............................f(2006/2007)=?
a.1004 b.1003 c.1003.5 d.1004.5
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2 Answers
66Let a = 2007, then for the function
f(x) = axax+√a,
Prove that f(x) + f(1-x) = 1.
Using this result we have
f(1/2007) + f(2006/2007) = f(1/2007) + f(1-1/2007) =1
Similarly,
f(2/2007) + f(2005/2007) = 1
f(3/2007) + f(2004/2007) = 1
.......
f(1002/2007) + f(1005/2007) = 1
f(1003/2007) + f(1004/2007) = 1
Adding them we get the required sum as 1003. Thus, (b)